Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The potential ($V$) at any axial point, at $2$ m distance ($r$) from the centre of the dipole of dipole moment vector $\vec{P}$ of magnitude, $4 \times 10^{-6}$ C m, is $\pm 9 \times 10^3$ V.
(Take $\dfrac{1}{4\pi\epsilon_0} = 9 \times 10^9$ SI units)
Reason R : $V = \pm\dfrac{2P}{4\pi\epsilon_0 r^2}$, where $r$ is the distance of any axial point, situated at $2$ m from the centre of the dipole.
In the light of the above statements, choose the correct answer from the options given below:
Answer: (A) A is true but R is false.
Concept. Axial potential of a short dipole: $V = \pm\dfrac{P}{4\pi\epsilon_0r^2}$.
Step 1. Assertion. $\dfrac{9 \times 10^9 \times 4 \times 10^{-6}}{4} = 9 \times 10^3$ V → true.
Step 2. Reason. The extra factor 2 belongs to the axial field ($\propto r^{-3}$) → false.
Answer. A is true but R is false (Option A).
Solution by Sreeraj P, M.Sc Physics